Answer :

Sure! To find the degree of the polynomial [tex]\(-4x^9 - 6 + 4x^8 + 6x^6\)[/tex], we can follow these steps:

1. Identify the terms in the polynomial: The polynomial provided is [tex]\(-4x^9 - 6 + 4x^8 + 6x^6\)[/tex]. Each term of the polynomial can be written with its corresponding power of [tex]\(x\)[/tex]:
- [tex]\(-4x^9\)[/tex]
- [tex]\(-6\)[/tex] (which can be written as [tex]\(-6x^0\)[/tex])
- [tex]\(4x^8\)[/tex]
- [tex]\(6x^6\)[/tex]

2. Determine the exponents of [tex]\(x\)[/tex] in each term:
- The first term, [tex]\(-4x^9\)[/tex], has an exponent of 9.
- The second term, [tex]\(-6\)[/tex] (or [tex]\(-6x^0\)[/tex]), has an exponent of 0.
- The third term, [tex]\(4x^8\)[/tex], has an exponent of 8.
- The fourth term, [tex]\(6x^6\)[/tex], has an exponent of 6.

3. Identify the highest exponent:
- The exponents we identified are 9, 0, 8, and 6.
- Among these, the highest exponent is 9.

4. Conclusion:
- The degree of a polynomial is the highest exponent of [tex]\(x\)[/tex] present among its terms.
- Therefore, the degree of the polynomial [tex]\(-4x^9 - 6 + 4x^8 + 6x^6\)[/tex] is 9.

So, the degree of the polynomial [tex]\(-4x^9 - 6 + 4x^8 + 6x^6\)[/tex] is 9.

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